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Translativity of a summation method

The property of the method consisting in the preservation of summability of a series after adding to or deleting from it a finite number of terms. More precisely, a summation method is said to be translative if the summability of the series

to the sum implies that the series

is summable by the same method to the sum , and conversely. For a summation method defined by transformation of the sequence into a sequence or function, the property of translativity consists of the equivalence of the conditions

and conversely. In cases when such an inference only holds in one direction, the method is called right translative if (1) implies (2) but the converse is false, or left translative if (2) implies (1) but the converse is false.

References

How to Cite This Entry: Translativity of a summation method. I.I. Volkov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Translativity_of_a_summation_method&oldid=17808

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098